Find the exponential function that passes through the two given points (0,7)and (6,8).

Question

Find the exponential function  that passes through the two given points (0,7)and (6,8).

Quizplus · Accepted Answer

We want to find an exponential function of the form $y = ab^x$ that passes through the points $(0,7)$ and $(6,8)$. Plugging in the first point, we get:
$$7 = ab^0 = a$$
So our function is of the form $y = 7b^x$. Now plugging in the second point, we get:
$$8 = 7b^6 \quad\Rightarrow\quad b = \sqrt[\leftroot{-2}\uproot{2}6]{\frac{8}{7}}$$
So our function is $y = 7\left(\sqrt[\leftroot{-2}\uproot{2}6]{\frac{8}{7}}\right)^x$, which matches choice B.

Find the Exponential Function That Passes Through the Two